Bayesian designs for hierarchical linear models
Bayesian designs for hierarchical linear models
Two Bayesian optimal design criteria for hierarchical linear models are discussed – the ?? criterion for the estimation of individual-level parameters ?, and the ?? criterion for the estimation of hyperparameters ?. We focus on a specific case in which all subjects receive the same set of treatments and in which the covariates are independent of treatments. We obtain the explicit structure of ??- and ??- optimal continuous (approximate) designs for the case of independent random effects, and for some special cases of correlated random effects. Through examples and simulations, we compare ??- and ??-optimal designs under more gen- eral scenarios of correlated random effects. While orthogonal designs are often ??-optimal even when the random effects are correlated, ??-optimal designs tend to be nonorthogonal and unbalanced. In our study of the robustness of ??- and ??-optimal designs, both types of designs are found to be insensitive to various specifications of the response errors and the vari- ances of the random effects, but sensitive to the specifications of the signs of the correlations of the random effects.
393-417
Liu, Qing
83a2f342-7e29-4277-a3a8-800c7d034287
Dean, Angela
9c90540a-cdf4-44ce-9d34-6b7b495a1ea3
Allenby, Gregory
9bf25e20-b988-488f-b71a-2bf757ff7c31
January 2012
Liu, Qing
83a2f342-7e29-4277-a3a8-800c7d034287
Dean, Angela
9c90540a-cdf4-44ce-9d34-6b7b495a1ea3
Allenby, Gregory
9bf25e20-b988-488f-b71a-2bf757ff7c31
Liu, Qing, Dean, Angela and Allenby, Gregory
(2012)
Bayesian designs for hierarchical linear models.
Statistica Sinica, 22 (1), .
(doi:10.5705/ss.2009.319).
Abstract
Two Bayesian optimal design criteria for hierarchical linear models are discussed – the ?? criterion for the estimation of individual-level parameters ?, and the ?? criterion for the estimation of hyperparameters ?. We focus on a specific case in which all subjects receive the same set of treatments and in which the covariates are independent of treatments. We obtain the explicit structure of ??- and ??- optimal continuous (approximate) designs for the case of independent random effects, and for some special cases of correlated random effects. Through examples and simulations, we compare ??- and ??-optimal designs under more gen- eral scenarios of correlated random effects. While orthogonal designs are often ??-optimal even when the random effects are correlated, ??-optimal designs tend to be nonorthogonal and unbalanced. In our study of the robustness of ??- and ??-optimal designs, both types of designs are found to be insensitive to various specifications of the response errors and the vari- ances of the random effects, but sensitive to the specifications of the signs of the correlations of the random effects.
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Published date: January 2012
Organisations:
Statistics, Statistical Sciences Research Institute
Identifiers
Local EPrints ID: 339777
URI: http://eprints.soton.ac.uk/id/eprint/339777
ISSN: 1017-0405
PURE UUID: 4934c454-11b9-4a75-a5b3-8f2feac8260d
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Date deposited: 30 May 2012 11:10
Last modified: 14 Mar 2024 11:15
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Author:
Qing Liu
Author:
Angela Dean
Author:
Gregory Allenby
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